Podcast with Bob Coecke, Chief Scientist at Quantinuum

Transcripts

Yuval Boger: Hello, Bob. And thank you for joining me today.

Bob Coecke: It’s pleasure.

Yuval: So who are you and what do you do?

Bob: Okay, so I’m Bob. That’s one thing. Currently, I’m Chief Scientist at Quantinuum. Before that, I was Chief Scientist at Cambridge Quantum before the merger with Honeywell Quantum Systems. And before that, I was a faculty at Oxford University, where I’ve been for some 20 years, mostly as a full professor, and I built a big group there in computer science, so 50 people. And by training, a physicist. But I’ve been pretty much all over the place, to be honest. I am. And since recently, I’m also a distinguished visiting Research Chair at the Perimeter Institute for Theoretical Physics in Canada.

Yuval: Well, it’s an honor to have you, and I think that amongst your other accomplishments, you’re also a book author, and you have a book that’s coming out. Maybe you can tell me a little bit about that, please?

Bob: Yes, there’s two books actually. I Had a book called Picturing Quantum Processes, which I think came out in 2017. I wrote with Aleks Kissinger. And there was a book full of diagrams showing that you can actually translate all of quantum theory in diagrammatic languages. But it was a university-level book. It was something we wrote for the course that Aleks and I were giving at Computer Science Oxford University. I mean, I think any younger graduate could take it, but we were pretty much teaching it at a post-grad level at the time.

Now there’s a new book out with Stephano Gogioso called Quantum in Pictures. And there, we’ve taken away any mathematical barrier so that this should be a broadly accessible book. We had, for example, teenagers in mind, maybe younger. Who knows? And the amateur doesn’t have a math background but is very interested in physics or the professional, because there’re STEM in there that’s actually cutting-edge new too.

Yuval: The book seems to introduce ZX-calculus, I think, through images. Are you targeting it for a particular age group? And once they finish the book, do you expect them to then move into tensors and more sophisticated math? Or …

Bob: The interesting thing is that there is nothing more sophisticated than you’ll find in that book for teenagers because this entire field, and that’s how I started and came into it, was through category theory. Category theory’s sort of considered the most sophisticated maths in the world. Most abstract, for sure. So I mean, I started this in 2003, reformulating quantum theory in a new way, an entirely new way, which I mean, I can elaborate on that later. But it turned out that you could equivalently do this kind of abstract math by just drawing pictures.

This was a very new result from the late ’90s that you could do this. And this traces back to work Penrose did in the ’60s and the ’70s where he started to draw tensor notation as pictures. So it’s highly nontrivial stuff. And the last couple of years, this particular math, even though we use it as an educational vehicle, also is being used widespreadly now in quantum industry to tackle problems of complexities that you simply can’t handle otherwise. So it’s bold, in a way, cutting-edge quantum text, and it makes quantum stuff accessible to a much broader audience.

Yuval: I didn’t mean to suggest that it was simplistic. I understand that it …

Bob: Let me say something to you. The international community, quantum computing community, they were very suspicious because it looked simplistic. They said, “This is never going to be useful for anything.” And the quantum computing companies, when they had to start dealing with complex problems, they kind of realized that this was the perfect language to do so.

For example, a company like PsiQuantum, which is the biggest quantum photonics company, it’s spoken language now. This is the language they speak there. And the cherry on the cake was a few weeks ago when Peter Shor, the person who came up with the factoring algorithm and all that, published a paper on ZX-calculus saying how good it was and all that. So it’s taken the community a while because people just couldn’t believe that something looking that simple could ever be useful for something important.

Yuval: And in the book you introduce quantum gates as spiders. Is the spiders terminology used in academic research as well or do they start calling it something else?

Bob: I mean, we start to use this term already in the previous book, which is a little bit more academically, so to say. Mostly people now use them in academics everywhere where they’re dealing with these types. So that’s a word which is state more or less. Now there’s a good reason for that because the official previous technical term, which you would find in my early papers… I’m trying not to get it wrong because it’s not easy. Dagger special commutative Frobenius algebra. And actually, Frobenius algebra is even. You said dagger special commutative Frobenius monoid, something like that. So I mean, it’s kind of a mouthful. It’s not very convenient. And so people just went to spiders.

Yuval: And through this diagram it seems that it’s easier to simplify quantum circuits and to optimize them so you can get fewer gates and lower depth of the circuit. Is that correct?

Bob: Yes. So basically what happens there is quantum circuits are typically made up of single-qubit gates or two-qubit gates. And then what ZX-calculus does, it breaks your two-qubit gates up into smaller things, which is typically a CNOT or something like that, your two-qubit gates, which is much more easy to reason with than the gate as a whole. So you break something that’s quite complex into two pieces, and these two pieces turn out to be very simple, and then you can show that also the phase gates and all that, sort of come naturally with these pieces. So you end up with a little graph calculus.

And yeah, it makes circuit simplification much easier. For example, in quantum optics, in photonics has photonic quantum computer, the error correction becomes much easier. That’s also what Shor was advertising. We now should use these things for error correction too. They have been used by Google for surface codes and things like that. Lots of practical things which now come up in quantum computing. And myself, these diagrams led to the field quantum natural language processing. It would never have come about without the diagrams. There’s no way anybody would now even be doing this on a quantum computer without the diagrams.

Yuval: The diagrams refer to gate-based quantum computers. I’m wondering, is there an analogy for the analog computers, the analog Hamiltonian simulation type?

Bob: Okay. So recently, people sort of figured out how to exponentiate and integrate and differentiate Hamiltonians in ZX-calculus. It’s a very new thing. This is from 2022. So things are moving in that direction for sure, and they’ve been used for quantum machine learning. Okay. You mentioned gate-based quantum computing. So there is another paradigm which most photonics companies are doing, which is measurement-based quantum computing. And the interesting historical thing is that in 2007, Ross Duncan, who’s the head of software at Quantinuum, and myself, we came up with ZX-calculus by actually looking at measurement-based quantum computing, not gate-based quantum computing. And the measurement-based were all the photonics people use, and it’s not a surprise. They were the first to completely starting to adopt this in quantum industry as their language because it was kind of made for them, but then it turned out to be good for gate-based too and some other things.

Yuval: You mentioned quantum natural language processing and natural language processing is very much in the news these days with ChatGPT and all these train models. How is quantum NLP different and what type of better results might you be able to expect one day with quantum NLP?

Bob: So historically, this direction started for me… I mean, I had no background whatsoever in linguistics, natural language processing, but I was developing this stuff you find in our books, which is technically called categorical quantum mechanics. It’s a heavy name, so we call it now quantum picturalism or quantum pictures. But initially, it was categorical quantum mechanics.

I was developing this, and I gave a talk about this in 2005 at McGill University and in the audience was Jim Lambek, who is somebody who wrote a paper in 1956, The Mathematics of Sentence Structure, which is very similar and created a lot of the computational linguistics field. And he saw me talking about quantum teleportation in pictures, like, “You finally did the new book,” and all that. He saw presenting quantum teleportation, and he said, “Hey, Bob. This is grammar.” I said, “No, Jim. This is quantum teleportation. This is physics.” “No, no, Bob. This is grammar.”

And he was right because through the right glasses, which are these glasses of category theory, which I was wearing at the time, grammatical structure and description of structure in language is exactly the same as the sort of math you used to describe quantum teleportation in pictures. It’s the same thing. Exactly the same thing. I mean, a bit later, Steve Clark, who’s now the head of AI at Quantinuum, who was a colleague then in University of Oxford of me, he explained the problem people had at the time in language theory. We had theories for grammar. We had theories for meaning like, now, ChatGPT and all these GPTs using which are vector bearings, but they didn’t know how to combine them. They didn’t know, for example, when you know the meaning of the words and grammatical structure, can we produce something representing the meaning of an old sentence, an entire sentence?

It’s a very natural thing. It’s something we humans can do very easily. We do it naturally, but there was no theory there. And then we basically following Jim Lambek’s observation; we just used the diagrammatic quantum formalism to build a new theory of language. At the time, we weren’t thinking at all about quantum computers. We had no quantum computers in mind whatsoever. But yeah, then later, when the quantum computers came, I mean, it was a natural thing to do. And because of this extra structure, we could actually do something that nobody expected. Train a quantum computer to understand some sentences and to understand some words and then do something like question and answering.

I mean, it was a complete shock for me that this was even possible in any way. But yeah, we did it. We did in 2020. And what we are hoping to do is to bring back a little bit more structure in AI or machine learning or whatever you call it, because, at the moment, it’s just this black-box thing. Nobody knows what’s happening actually. I mean, it looks all very impressive in the way it can simulate how a person would speak. So it’s very, very impressive. But we don’t understand how it goes. I mean, there are also issues whether you could imagine whether such a thing could actually ever be creative in some way. I mean, a lot of the machine learning field, AI field is now going into the direction of VI. We probably need to bring in some more structure again because we can’t just go brute force all the way. And that’s kind of what we are bringing in.

Yuval: And if you look at the quantum NLP today with today’s computers, what is quantum NLP able to achieve in terms of complexity or results?

Bob: So, I mean, the latest published experiments were done by IBM because there’s like two or three teams at IBM now doing our form of QNLP. And what they did is what they call mid-scale machine learning. So it’s not large scale yet, but it’s mid-scale yet, and the results are really good, like we get nice convergences. Of course, the scale is not big enough to do what we actually hope to, that we can really be so much better at than what current machine learning does. And that’s really deep understanding of a text or something. Genuine, deep understanding of a text. Long-range correlations, they’re really bad at the moment, the language models. They’re good at short… And also, they don’t update. They’re very static, like ChatGPT doesn’t know what happened in the last two years or something like that, or last year and a half. I can’t remember exactly the date. And our systems would naturally update all the time. So they would be different. So we are expecting a lot of advantages, but for that scale, we need a lot bigger machines.

Something I didn’t say is, so we had these nice theory, but we were struggling on classical machines because it’s quantum models. So just like chemistry, just like materials, they weren’t seen on the quantum computer. So that was a problem we had at that time. So it’s an interesting area where you expect the same advantages as quantum chemistry and quantum materials, but we are not talking about quantum substance. We are talking about language. And We are doing more general cognitive stuff too, and then going to more general AI and things like that. So it’s not just that we restrict ourselves to language.

Yuval: As a chief scientist at Quantinuum, what else are you working on, if you can tell us?

Bob: What I am working on, I mean, I just published a book. So the main thing I’ve been working on the last year, and year and a half, which may sound a bit weird, is really on new theories of languages beyond the one we came up with in 2008 and 2009. And we got a new language form. Listen, we put out a blog post, I think, one or two weeks ago. It was a medium blog, and it was something called Looking for University of Language. So by actually working with these quantum computers, we actually had to turn language, which is normally written on the line, into a quantum circuit. So we turn something one-dimension into something two-dimension. And then, by doing this properly and getting all the mathematics right, we discovered that in doing so, differences between languages, like how your words would be differently ordered in one language as in another language and your punctuation would be completely different, that all these differences vanished when we went to the circuits.

So we kind of found something underneath language, which seems to be much more universal than whatever we speak. And also stylistic differences vanish. And so that’s something we are working on a lot now because it’s a completely different thing. And also, today at my office downstairs, Eduardo Miranda arrived. So Eduardo Miranda is somebody who’s been playing around with quantum computers to do music. I mean, I’ve been doing this before with him too. We created something called quanthoven, which was a way to generate music with quantum computer of a certain genre. Again, small scale, but we did it. We actually produced new music with a quantum computer. And then a very funny thing happened. This became number one on some classical charts. So anyway, this is what we’re going to work a little bit on this week too with Eduardo, doing some more quantum music. Yeah, I mean, I’m doing lots of stuff actually. Too much. It keeps me awake.

Yuval: And I’ve had Eduardo on this podcast as well, so I enjoy it. Absolutely. You made the transition from a professor to industry. It must be different. Is that a path that you would recommend for others?

Bob: That’s an interesting question. And then the thing is, you should have asked me this question before I did it, record my answer, and then ask it now and record my answer. And they would be very different. I can tell you that. So I was a very long time in academia and I’ve got a feeling now that I’ve actually regained academic freedom, which may sound contradictory to what most people would tell you, but actually I have a lot more freedom now. Just to say, this book which came out now, I’ve been trying to finish with Stefano for many years at university, and I just couldn’t find the time or support. And now it’s published by Quantinuum with a lot of support. We got a lot of support for the publication of this book.

So interestingly, initially, I mean, I mentioned that there was some sort of skepticism in the community about whether this stuff would be ever useful. So the reason we initially started to write this was to set up an experiment in which we take, on the one hand, Oxford University students taking a regular quantum course, and on the other end, teenagers take learning from this book, and then give them the same exam and see who out-performs who. So that was the experiment we had in mind, but we just couldn’t find any support in academia. Hardly any support to do it. And now it’s all supported by actually mainly the quantum industry, not just Quantinuum, but also IBM is helping with it.

So the industry is much more keen for things like this book, which is all about inclusivity, and then you would actually find in academia, which is very interesting. And also, the sort of stuff I’m doing now with QNLP, would’ve been impossible in academia because the nature of the jobs and the nature of people’s careers is very different. I mean, I could write a book about it. I could write a book about it, but I mean, a lot of people actually are full of my example and gave up faculty positions, and quite a number who are now working in my team.

Yuval: When you look at the advancements in the quantum industry, obviously Quantinuum has a lot of resources, but the industry, best of all, has more minds and more money and more directions that are working on. What would you like to see other companies in the industry doing that they’re not doing right now?

Bob: I mean, what I’ve noticed is that we have a good chunk of the industry; they’re actually collaborating a lot more than you sometimes find in academia, where universities are competing against each other for rankings, people are competing against each other for getting the paper the first time out, and things like that. So I mean, something that surprised me is really this collaborative edge, and that’s something that needs to continue. And some companies aren’t as collaborative as other ones.

Let’s put it like that. And some companies are very, very honest in what they’re doing and very, very straight. And these are typically the big ones. The big ones who are not necessarily funded by venture capital. So sometimes those funded by vendor capital, by no means all, they kind of give the whole field a bad name by saying things they shouldn’t be saying. And that’s maybe a little bit too much of that. But on the other hand, if you, for example, look at the video of Tony Uttley at Q2B, you get the most honest and direct representation of what actually is going on at the moment. For example, in Quantinuum, what we can do, what we can’t do, what we expect. And a lot of people are like that.

Yuval: Very good. So I want to end with a hypothetical question. So if you could have dinner with one of the quantum greats, dead or alive, who would that person be?

Bob: Oh, well, that would be, I guess, Schrodinger.

Yuval: And why?

Bob: So one of the things, which this book also puts forward in all these diagrammatic formalism, is a new worldview really, which departs from what is almost 2,500-year-old worldview going back to Aristotle and Parmenides and all these people, where you think about the thing of how it is made up. So if you understand the physics thing, you go to smaller particles inside. If you want to understand human, you start doing autonomy. You understand maths, you break it down into its elements and set theory. So the kind of maths which we have in our book, it actually puts composition of systems on the first place. You’ve got things, and they also understand things by what happens if you bring them together. Like you bring two people together, what is the relationship which emerges and all that?

And this sort of more relational mathematics, I mean, Schrodinger actually put this forward in somewhere in ’35 by saying actually, the most important thing in quantum is not measurement, but is tensor product. And to some extent, all that I’ve done is basically taking that idea seriously and translating all of quantum mechanics in tensor language only, composition language only. So I mean, Schrodinger’s done a lot of bad things in his life, very bad things. It’s maybe not the most… But he was an hypothetical question, assuming that Schrodinger didn’t do bad things in his life, let’s put it… It was just about the scientific idea. Yeah.

Yuval: Absolutely. And maybe if he saw your book, it would not be Schrodinger’s cat, but Schrodinger’s spider.

Bob: Yeah.

Yuval: So we covered a lot of topics today, from quantum natural language processing to unified model of languages and spiders and ZX-calculus. Is there anything else that you’d like to share with the community before we end our discussion today?

Bob: No, no, it’s all fine. Just go and buy the book. It’s available since today. Since today, which is probably a different day from when you actually will hear this, but just a few hours to go, it just came on the market. So it’s now available for everybody pretty much in every country instantly.

Yuval: Excellent. I certainly enjoyed reading it, and I hope my listeners will as well. Bob, thank you so much for joining me today.

Bob: Thank you. Bye.

Yuval Boger is an executive working at the intersection of quantum technology and business. Known as the “Superposition Guy” as well as the original “Qubit Guy,” he can be reached on LinkedIn or at this email.

March 13, 2023